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प्रश्न
Write the vector equation of a line passing through a point having position vector \[\overrightarrow{\alpha}\] and parallel to vector \[\overrightarrow{\beta}\] .
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उत्तर
The vector equation of the line passing through the point having position vector \[\overrightarrow{\alpha}\] and parallel to vector \[\overrightarrow{\beta}\] is \[\overrightarrow{r} = \overrightarrow{\alpha} + \lambda \overrightarrow{\beta}\]
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Determine whether the following pair of lines intersect or not:
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\[\vec{r} = \left( 2 \hat{i} - 5 \hat{j} + \hat{k} \right) + \lambda\left( 3 \hat{i} + 2 \hat{j} + 6 \hat{k} \right)\] and \[\vec{r} = 7 \hat{i} - 6 \hat{k} + \mu\left( \hat{i} + 2 \hat{j} + 2 \hat{k} \right)\]
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Equation of a line passing through (1, 1, 1) and parallel to z-axis is ______.
